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Book Market Risk Analysis  Value at Risk Models

Download or read book Market Risk Analysis Value at Risk Models written by Carol Alexander and published by John Wiley & Sons. This book was released on 2009-02-09 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading market risk academic, Professor Carol Alexander, Value-at-Risk Models forms part four of the Market Risk Analysis four volume set. Building on the three previous volumes this book provides by far the most comprehensive, rigorous and detailed treatment of market VaR models. It rests on the basic knowledge of financial mathematics and statistics gained from Volume I, of factor models, principal component analysis, statistical models of volatility and correlation and copulas from Volume II and, from Volume III, knowledge of pricing and hedging financial instruments and of mapping portfolios of similar instruments to risk factors. A unifying characteristic of the series is the pedagogical approach to practical examples that are relevant to market risk analysis in practice. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Parametric linear value at risk (VaR)models: normal, Student t and normal mixture and their expected tail loss (ETL); New formulae for VaR based on autocorrelated returns; Historical simulation VaR models: how to scale historical VaR and volatility adjusted historical VaR; Monte Carlo simulation VaR models based on multivariate normal and Student t distributions, and based on copulas; Examples and case studies of numerous applications to interest rate sensitive, equity, commodity and international portfolios; Decomposition of systematic VaR of large portfolios into standard alone and marginal VaR components; Backtesting and the assessment of risk model risk; Hypothetical factor push and historical stress tests, and stress testing based on VaR and ETL.

Book Measuring Market Risk with Value at Risk

Download or read book Measuring Market Risk with Value at Risk written by Pietro Penza and published by John Wiley & Sons. This book was released on 2001 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book, Measuring Market Risk with Value at Risk by Vipul Bansal and Pietro Penza, has three advantages over earlier works on the subject. First, it takes a decidedly global approach-an essential ingredient for any comprehensive work on market risk. Second, it ties the scientifically grounded, yet intuitively appealing, VaR measure to earlier, more idiosyncratic measures of market risk that are used in specific market environs (e.g., duration in fixed income). Finally, it encompasses all of the accepted approaches to calculating a VaR measure and presents them in a clearly explained fashion with supporting illustrations and completely worked-out examples." -from the Foreword by John F. Marshall, PhD, Principal, Marshall, Tucker & Associates, LLC "Measuring Market Risk with Value at Risk offers a much-needed intellectual bridge, a translation from the esoteric realm of mathematical finance to the domain of financial managers who seek guidance in applying developments from this important field of research as well as that of MBA-level graduate instruction. I believe the authors have done a commendable job of providing a carefully crafted, highly readable, and most useful work, and intend to recommend it to all those involved in business risk management applications." -Anthony F. Herbst, PhD, Professor of Finance and C.R. and D.S. Carter Chair, The University of Texas, El Paso and Founding editor of The Journal of Financial Engineering (1991-1998) "Finally there's a book that strikes a balance between rigor and application in the area of risk management in the banking industry. This innovative book is a MUST for both novices and professionals alike." -Robert P. Yuyuenyongwatana, PhD, Associate Professor of Finance, Cameron University "Measuring Market Risk with Value at Risk is one of the most complete discussions of this emerging topic in finance that I have seen. The authors develop a logical and rigorous framework for using VaR models, providing both historical references and analytical applications." -Kevin Wynne, PhD, Associate Professor of Finance, Lubin School of Business, Pace University

Book Market Risk Analysis  Boxset

Download or read book Market Risk Analysis Boxset written by Carol Alexander and published by John Wiley & Sons. This book was released on 2009-02-24 with total page 1691 pages. Available in PDF, EPUB and Kindle. Book excerpt: Market Risk Analysis is the most comprehensive, rigorous and detailed resource available on market risk analysis. Written as a series of four interlinked volumes each title is self-contained, although numerous cross-references to other volumes enable readers to obtain further background knowledge and information about financial applications. Volume I: Quantitative Methods in Finance covers the essential mathematical and financial background for subsequent volumes. Although many readers will already be familiar with this material, few competing texts contain such a complete and pedagogical exposition of all the basic quantitative concepts required for market risk analysis. There are six comprehensive chapters covering all the calculus, linear algebra, probability and statistics, numerical methods and portfolio mathematics that are necessary for market risk analysis. This is an ideal background text for a Masters course in finance. Volume II: Practical Financial Econometrics provides a detailed understanding of financial econometrics, with applications to asset pricing and fund management as well as to market risk analysis. It covers equity factor models, including a detailed analysis of the Barra model and tracking error, principal component analysis, volatility and correlation, GARCH, cointegration, copulas, Markov switching, quantile regression, discrete choice models, non-linear regression, forecasting and model evaluation. Volume III: Pricing, Hedging and Trading Financial Instruments has five very long chapters on the pricing, hedging and trading of bonds and swaps, futures and forwards, options and volatility as well detailed descriptions of mapping portfolios of these financial instruments to their risk factors. There are numerous examples, all coded in interactive Excel spreadsheets, including many pricing formulae for exotic options but excluding the calibration of stochastic volatility models, for which Matlab code is provided. The chapters on options and volatility together constitute 50% of the book, the slightly longer chapter on volatility concentrating on the dynamic properties the two volatility surfaces the implied and the local volatility surfaces that accompany an option pricing model, with particular reference to hedging. Volume IV: Value at Risk Models builds on the three previous volumes to provide by far the most comprehensive and detailed treatment of market VaR models that is currently available in any textbook. The exposition starts at an elementary level but, as in all the other volumes, the pedagogical approach accompanied by numerous interactive Excel spreadsheets allows readers to experience the application of parametric linear, historical simulation and Monte Carlo VaR models to increasingly complex portfolios. Starting with simple positions, after a few chapters we apply value-at-risk models to interest rate sensitive portfolios, large international securities portfolios, commodity futures, path dependent options and much else. This rigorous treatment includes many new results and applications to regulatory and economic capital allocation, measurement of VaR model risk and stress testing.

Book Market Risk Analysis  Practical Financial Econometrics

Download or read book Market Risk Analysis Practical Financial Econometrics written by Carol Alexander and published by John Wiley & Sons. This book was released on 2008-05-27 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading market risk academic, Professor Carol Alexander, Practical Financial Econometrics forms part two of the Market Risk Analysis four volume set. It introduces the econometric techniques that are commonly applied to finance with a critical and selective exposition, emphasising the areas of econometrics, such as GARCH, cointegration and copulas that are required for resolving problems in market risk analysis. The book covers material for a one-semester graduate course in applied financial econometrics in a very pedagogical fashion as each time a concept is introduced an empirical example is given, and whenever possible this is illustrated with an Excel spreadsheet. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM. Empirical examples and case studies specific to this volume include: Factor analysis with orthogonal regressions and using principal component factors; Estimation of symmetric and asymmetric, normal and Student t GARCH and E-GARCH parameters; Normal, Student t, Gumbel, Clayton, normal mixture copula densities, and simulations from these copulas with application to VaR and portfolio optimization; Principal component analysis of yield curves with applications to portfolio immunization and asset/liability management; Simulation of normal mixture and Markov switching GARCH returns; Cointegration based index tracking and pairs trading, with error correction and impulse response modelling; Markov switching regression models (Eviews code); GARCH term structure forecasting with volatility targeting; Non-linear quantile regressions with applications to hedging.

Book Market Risk Analysis  Quantitative Methods in Finance

Download or read book Market Risk Analysis Quantitative Methods in Finance written by Carol Alexander and published by John Wiley & Sons. This book was released on 2008-04-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading market risk academic, Professor Carol Alexander, Quantitative Methods in Finance forms part one of the Market Risk Analysis four volume set. Starting from the basics, this book helps readers to take the first step towards becoming a properly qualified financial risk manager and asset manager, roles that are currently in huge demand. Accessible to intelligent readers with a moderate understanding of mathematics at high school level or to anyone with a university degree in mathematics, physics or engineering, no prior knowledge of finance is necessary. Instead the emphasis is on understanding ideas rather than on mathematical rigour, meaning that this book offers a fast-track introduction to financial analysis for readers with some quantitative background, highlighting those areas of mathematics that are particularly relevant to solving problems in financial risk management and asset management. Unique to this book is a focus on both continuous and discrete time finance so that Quantitative Methods in Finance is not only about the application of mathematics to finance; it also explains, in very pedagogical terms, how the continuous time and discrete time finance disciplines meet, providing a comprehensive, highly accessible guide which will provide readers with the tools to start applying their knowledge immediately. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Principal component analysis of European equity indices; Calibration of Student t distribution by maximum likelihood; Orthogonal regression and estimation of equity factor models; Simulations of geometric Brownian motion, and of correlated Student t variables; Pricing European and American options with binomial trees, and European options with the Black-Scholes-Merton formula; Cubic spline fitting of yields curves and implied volatilities; Solution of Markowitz problem with no short sales and other constraints; Calculation of risk adjusted performance metrics including generalised Sharpe ratio, omega and kappa indices.

Book Financial Risk Forecasting

Download or read book Financial Risk Forecasting written by Jon Danielsson and published by John Wiley & Sons. This book was released on 2011-04-20 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial Risk Forecasting is a complete introduction to practical quantitative risk management, with a focus on market risk. Derived from the authors teaching notes and years spent training practitioners in risk management techniques, it brings together the three key disciplines of finance, statistics and modeling (programming), to provide a thorough grounding in risk management techniques. Written by renowned risk expert Jon Danielsson, the book begins with an introduction to financial markets and market prices, volatility clusters, fat tails and nonlinear dependence. It then goes on to present volatility forecasting with both univatiate and multivatiate methods, discussing the various methods used by industry, with a special focus on the GARCH family of models. The evaluation of the quality of forecasts is discussed in detail. Next, the main concepts in risk and models to forecast risk are discussed, especially volatility, value-at-risk and expected shortfall. The focus is both on risk in basic assets such as stocks and foreign exchange, but also calculations of risk in bonds and options, with analytical methods such as delta-normal VaR and duration-normal VaR and Monte Carlo simulation. The book then moves on to the evaluation of risk models with methods like backtesting, followed by a discussion on stress testing. The book concludes by focussing on the forecasting of risk in very large and uncommon events with extreme value theory and considering the underlying assumptions behind almost every risk model in practical use – that risk is exogenous – and what happens when those assumptions are violated. Every method presented brings together theoretical discussion and derivation of key equations and a discussion of issues in practical implementation. Each method is implemented in both MATLAB and R, two of the most commonly used mathematical programming languages for risk forecasting with which the reader can implement the models illustrated in the book. The book includes four appendices. The first introduces basic concepts in statistics and financial time series referred to throughout the book. The second and third introduce R and MATLAB, providing a discussion of the basic implementation of the software packages. And the final looks at the concept of maximum likelihood, especially issues in implementation and testing. The book is accompanied by a website - www.financialriskforecasting.com – which features downloadable code as used in the book.

Book Understanding Market  Credit  and Operational Risk

Download or read book Understanding Market Credit and Operational Risk written by Linda Allen and published by John Wiley & Sons. This book was released on 2009-02-04 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step, real world guide to the use of Value at Risk (VaR) models, this text applies the VaR approach to the measurement of market risk, credit risk and operational risk. The book describes and critiques proprietary models, illustrating them with practical examples drawn from actual case studies. Explaining the logic behind the economics and statistics, this technically sophisticated yet intuitive text should be an essential resource for all readers operating in a world of risk. Applies the Value at Risk approach to market, credit, and operational risk measurement. Illustrates models with real-world case studies. Features coverage of BIS bank capital requirements.

Book Hands On Value at Risk and Expected Shortfall

Download or read book Hands On Value at Risk and Expected Shortfall written by Martin Auer and published by Springer. This book was released on 2018-02-01 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a maximally simple market risk model that is still practical and main risk measures like the value-at-risk and the expected shortfall. It outlines the model's (i) underlying math, (ii) daily operation, and (iii) implementation, while stripping away statistical overhead to keep the concepts accessible. The author selects and weighs the various model features, motivating the choices under real-world constraints, and addresses the evermore important handling of regulatory requirements. The book targets not only practitioners new to the field but also experienced market risk operators by suggesting useful data analysis procedures and implementation details. It furthermore addresses market risk consumers such as managers, traders, and compliance officers by making the model behavior intuitively transparent. A very useful guide to the theoretical and practical aspects of implementing and operating a risk-monitoring system for a mid-size financial institution. It sets a common body of knowledge to facilitate communication between risk managers, computer and investment specialists by bridging their diverse backgrounds. Giovanni Barone-Adesi — Professor, Universitá della Svizzera italiana This unassuming and insightful book starts from the basics and plainly brings the reader up to speed on both theory and implementation. Shane Hegarty — Director Trade Floor Risk Management, Scotiabank Visit the book’s website at www.value-at-risk.com.

Book Risk Analysis and Portfolio Modelling

Download or read book Risk Analysis and Portfolio Modelling written by Elisa Luciano and published by MDPI. This book was released on 2019-10-16 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial Risk Measurement is a challenging task, because both the types of risk and the techniques evolve very quickly. This book collects a number of novel contributions to the measurement of financial risk, which address either non-fully explored risks or risk takers, and does so in a wide variety of empirical contexts.

Book The Value at risk Reference

Download or read book The Value at risk Reference written by Jon Danielsson and published by Risk. This book was released on 2007 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-stop reference pulling together leading published research and analysis about VaR and market risk. An invaluable summary for practitioners and researchers looking for an independent evaluation of VaR and insight into how and when it should be used.

Book Measuring Market Risk

Download or read book Measuring Market Risk written by Kevin Dowd and published by John Wiley & Sons. This book was released on 2003-02-28 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most up-to-date resource on market risk methodologies Financial professionals in both the front and back office require an understanding of market risk and how to manage it. Measuring Market Risk provides this understanding with an overview of the most recent innovations in Value at Risk (VaR) and Expected Tail Loss (ETL) estimation. This book is filled with clear and accessible explanations of complex issues that arise in risk measuring-from parametric versus nonparametric estimation to incre-mental and component risks. Measuring Market Risk also includes accompanying software written in Matlab—allowing the reader to simulate and run the examples in the book.

Book International Convergence of Capital Measurement and Capital Standards

Download or read book International Convergence of Capital Measurement and Capital Standards written by and published by Lulu.com. This book was released on 2004 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book The Financial Crisis Inquiry Report

Download or read book The Financial Crisis Inquiry Report written by Financial Crisis Inquiry Commission and published by Cosimo, Inc.. This book was released on 2011-05-01 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Financial Crisis Inquiry Report, published by the U.S. Government and the Financial Crisis Inquiry Commission in early 2011, is the official government report on the United States financial collapse and the review of major financial institutions that bankrupted and failed, or would have without help from the government. The commission and the report were implemented after Congress passed an act in 2009 to review and prevent fraudulent activity. The report details, among other things, the periods before, during, and after the crisis, what led up to it, and analyses of subprime mortgage lending, credit expansion and banking policies, the collapse of companies like Fannie Mae and Freddie Mac, and the federal bailouts of Lehman and AIG. It also discusses the aftermath of the fallout and our current state. This report should be of interest to anyone concerned about the financial situation in the U.S. and around the world.THE FINANCIAL CRISIS INQUIRY COMMISSION is an independent, bi-partisan, government-appointed panel of 10 people that was created to "examine the causes, domestic and global, of the current financial and economic crisis in the United States." It was established as part of the Fraud Enforcement and Recovery Act of 2009. The commission consisted of private citizens with expertise in economics and finance, banking, housing, market regulation, and consumer protection. They examined and reported on "the collapse of major financial institutions that failed or would have failed if not for exceptional assistance from the government."News Dissector DANNY SCHECHTER is a journalist, blogger and filmmaker. He has been reporting on economic crises since the 1980's when he was with ABC News. His film In Debt We Trust warned of the economic meltdown in 2006. He has since written three books on the subject including Plunder: Investigating Our Economic Calamity (Cosimo Books, 2008), and The Crime Of Our Time: Why Wall Street Is Not Too Big to Jail (Disinfo Books, 2011), a companion to his latest film Plunder The Crime Of Our Time. He can be reached online at www.newsdissector.com.

Book Handbook of Market Risk

Download or read book Handbook of Market Risk written by Christian Szylar and published by John Wiley & Sons. This book was released on 2013-10-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ONE-STOP GUIDE FOR THE THEORIES, APPLICATIONS, AND STATISTICAL METHODOLOGIES OF MARKET RISK Understanding and investigating the impacts of market risk on the financial landscape is crucial in preventing crises. Written by a hedge fund specialist, the Handbook of Market Risk is the comprehensive guide to the subject of market risk. Featuring a format that is accessible and convenient, the handbook employs numerous examples to underscore the application of the material in a real-world setting. The book starts by introducing the various methods to measure market risk while continuing to emphasize stress testing, liquidity, and interest rate implications. Covering topics intrinsic to understanding and applying market risk, the handbook features: An introduction to financial markets The historical perspective from market events and diverse mathematics to the value-at-risk Return and volatility estimates Diversification, portfolio risk, and efficient frontier The Capital Asset Pricing Model and the Arbitrage Pricing Theory The use of a fundamental multi-factors model Financial derivatives instruments Fixed income and interest rate risk Liquidity risk Alternative investments Stress testing and back testing Banks and Basel II/III The Handbook of Market Risk is a must-have resource for financial engineers, quantitative analysts, regulators, risk managers in investments banks, and large-scale consultancy groups advising banks on internal systems. The handbook is also an excellent text for academics teaching postgraduate courses on financial methodology.

Book Risk Modeling  Assessment  and Management

Download or read book Risk Modeling Assessment and Management written by Yacov Y. Haimes and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines timely multidisciplinary applications, problems, and case histories in risk modeling, assessment, and management Risk Modeling, Assessment, and Management, Third Edition describes the state of the art of risk analysis, a rapidly growing field with important applications in engineering, science, manufacturing, business, homeland security, management, and public policy. Unlike any other text on the subject, this definitive work applies the art and science of risk analysis to current and emergent engineering and socioeconomic problems. It clearly demonstrates how to quantify risk and construct probabilities for real-world decision-making problems, including a host of institutional, organizational, and political issues. Avoiding higher mathematics whenever possible, this important new edition presents basic concepts as well as advanced material. It incorporates numerous examples and case studies to illustrate the analytical methods under discussion and features restructured and updated chapters, as well as: A new chapter applying systems-driven and risk-based analysis to a variety of Homeland Security issues An accompanying FTP site—developed with Professor Joost Santos—that offers 150 example problems with an Instructor's Solution Manual and case studies from a variety of journals Case studies on the 9/11 attack and Hurricane Katrina An adaptive multiplayer Hierarchical Holographic Modeling (HHM) game added to Chapter Three This is an indispensable resource for academic, industry, and government professionals in such diverse areas as homeland and cyber security, healthcare, the environment, physical infrastructure systems, engineering, business, and more. It is also a valuable textbook for both undergraduate and graduate students in systems engineering and systems management courses with a focus on our uncertain world.

Book Financial Risk Management

Download or read book Financial Risk Management written by Jimmy Skoglund and published by John Wiley & Sons. This book was released on 2015-09-04 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: A global banking risk management guide geared toward the practitioner Financial Risk Management presents an in-depth look at banking risk on a global scale, including comprehensive examination of the U.S. Comprehensive Capital Analysis and Review, and the European Banking Authority stress tests. Written by the leaders of global banking risk products and management at SAS, this book provides the most up-to-date information and expert insight into real risk management. The discussion begins with an overview of methods for computing and managing a variety of risk, then moves into a review of the economic foundation of modern risk management and the growing importance of model risk management. Market risk, portfolio credit risk, counterparty credit risk, liquidity risk, profitability analysis, stress testing, and others are dissected and examined, arming you with the strategies you need to construct a robust risk management system. The book takes readers through a journey from basic market risk analysis to major recent advances in all financial risk disciplines seen in the banking industry. The quantitative methodologies are developed with ample business case discussions and examples illustrating how they are used in practice. Chapters devoted to firmwide risk and stress testing cross reference the different methodologies developed for the specific risk areas and explain how they work together at firmwide level. Since risk regulations have driven a lot of the recent practices, the book also relates to the current global regulations in the financial risk areas. Risk management is one of the fastest growing segments of the banking industry, fueled by banks' fundamental intermediary role in the global economy and the industry's profit-driven increase in risk-seeking behavior. This book is the product of the authors' experience in developing and implementing risk analytics in banks around the globe, giving you a comprehensive, quantitative-oriented risk management guide specifically for the practitioner. Compute and manage market, credit, asset, and liability risk Perform macroeconomic stress testing and act on the results Get up to date on regulatory practices and model risk management Examine the structure and construction of financial risk systems Delve into funds transfer pricing, profitability analysis, and more Quantitative capability is increasing with lightning speed, both methodologically and technologically. Risk professionals must keep pace with the changes, and exploit every tool at their disposal. Financial Risk Management is the practitioner's guide to anticipating, mitigating, and preventing risk in the modern banking industry.

Book Market Risk Analysis  Pricing  Hedging and Trading Financial Instruments

Download or read book Market Risk Analysis Pricing Hedging and Trading Financial Instruments written by Carol Alexander and published by Wiley. This book was released on 2008-06-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading market risk academic, Professor Carol Alexander, Pricing, Hedging and Trading Financial Instruments forms part three of the Market Risk Analysis four volume set. This book is an in-depth, practical and accessible guide to the models that are used for pricing and the strategies that are used for hedging financial instruments, and to the markets in which they trade. It provides a comprehensive, rigorous and accessible introduction to bonds, swaps, futures and forwards and options, including variance swaps, volatility indices and their futures and options, to stochastic volatility models and to modelling the implied and local volatility surfaces. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Duration-Convexity approximation to bond portfolios, and portfolio immunization; Pricing floaters and vanilla, basis and variance swaps; Coupon stripping and yield curve fitting; Proxy hedging, and hedging international securities and energy futures portfolios; Pricing models for European exotics, including barriers, Asians, look-backs, choosers, capped, contingent, power, quanto, compo, exchange, ‘best-of’ and spread options; Libor model calibration; Dynamic models for implied volatility based on principal component analysis; Calibration of stochastic volatility models (Matlab code); Simulations from stochastic volatility and jump models; Duration, PV01 and volatility invariant cash flow mappings; Delta-gamma-theta-vega mappings for options portfolios; Volatility beta mapping to volatility indices.